Theorems · Theorem · commutative algebra
IsLocalization.of_le_isUnit
∀ {R : Type u_1} [inst : CommSemiring R] {S : Submonoid R}, S ≤ IsUnit.submonoid R → IsLocalization S R- Defined in
- Mathlib.RingTheory.Localization.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Submonoidstatement and proof · cited by 3,086
- IsLocalizationstatement · cited by 636
- IsUnit.submonoidstatement and proof · cited by 56
- Function.bijective_idproof · cited by 36
- IsLocalization.of_le_isUnit_of_bijectiveproof · cited by 4
- Algebra.algebraMapSubmonoid_selfproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- RingHom.HoldsForLocalizationAway.of_bijectiveproof · cited by 2
- IsLocalization.at_unitsproof · cited by 0